Thursday, February 19, 2009

Deduction or Induction? A classic nerd debate

I've been working on my own game system, MUTT.  MUTT has a detective skill that I call "induction."  This is because I firmly believe that Sir Arthur Conan Doyle used the wrong word when describing Sherlock Holmes.

A good nerd-friend challenged me on this somewhat classic debate: whether Holmes induces or deduces his answers.  Below is the argument my discussion with him produced.

The word "deduction" has a variety of meanings, as anyone can find if they go to the dictionary.   Debating such meanings relative correctness would be pedantic and pointless.  However Sherlock Holmes is often held up as an example of deductive reasoning in a formal sense. IF we limit our discussion to that issue: does Holmes formally deduce his results, I think the answer has to be no.

I would suggest in fiormal terms a typical Holmes argument takes the following form:

(1) If P then Q
(2) If P then S
(3) If P then T

Q S and T are all true, there for the only reasonable conclusion is P.

He is certainly not alone in this reasoning. This is classic court-room stuff and even has a legal term-- "the preponderance of evidence." But is it, formally, deduction? By deductive reasoning it is clearly fallacious. Just because P is *an* explanation for Q S and T does not make it automatically the *right* explanation for Q S and T. In fact, there is no logical requirement that Q,S and T have the same cause at all, just so long as there are no other predicate statements that say the disparate causes cannot logically co-exist.

Holmes himself in fact shows us this when he describes his own methodology-- "when you have eliminated the impossible, whatever remains, however improbable, must be the truth." [4] In order for this claim to be logically true, it presupposes the omniscience to know all possibilities and impossibilities. What Holmes really means is "When I have eliminated every other possibility I can think of, the one left must be true." Which fits with his ego, but is hardly a logical conclusion.

SO either Holmes does a very bad job of formal deductive reasoning, or in fact engages in educated guesswork from specific bits of evidence leading to a theory of the whole cause, which would be reasoning by induction. I chose to believe the latter.


So what do YOU think?  Comments are open.



2 comments:

Andrew said...

Sir Arthur Conan Doyle convinced himself that the Cottingly Faries must have been real, because the alternative - that a pair of young girls could have fooled him with faked photographs - was obviously impossible. I believe this speaks volumes as to the validity of his approach.

Elizabeth J. Neal said...

We wield our logic with confidence, not noticing our occasional deductive errors. Before declaring that you are immune to such errors and skipping to the next chapter, please take ten minutes to attack the following problem: feng shui singapore